Problem: Graph this system of equations and solve. $-3x-4y = 8$ $2x-4y = -12$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Solution: Convert the first equation, $-3x-4y = 8$ , to slope-intercept form. $y = -\dfrac{3}{4} x - 2$ The y-intercept for the first equation is $-2$ , so the first line must pass through the point $(0, -2)$ The slope for the first equation is $-\dfrac{3}{4}$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move down (because it's negative) You must also move $4$ positions to the right. $4$ positions to the right. $3$ positions down from $(0, -2)$ is $(4, -5)$ Graph the blue line so it passes through $(0, -2)$ and $(4, -5)$ Convert the second equation, $2x-4y = -12$ , to slope-intercept form. $y = \dfrac{1}{2} x + 3$ The y-intercept for the second equation is $3$ , so the second line must pass through the point $(0, 3)$ The slope for the second equation is $\dfrac{1}{2}$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move up You must also move $2$ positions to the right. $2$ positions to the right. Graph the green line so it passes through $(0, 3)$ and $(2, 4)$ The solution is the point where the two lines intersect. The lines intersect at $(-4, 1)$.